What is the meaning of ##d\Omega## in solid angle integration?

[PreposterousUniverse]

Anyone have any idea how to perform the following two integrals?

$\int d\Omega n_{i}n_{j}$ and $\int d\Omega n_{i}n_{j}n_{k}n_{l}$

where the n is a unit vector.

 

[BvU]

Not if you don't provide some more context. The way it looks now (to me) it's nonsense ($n_in_j = \delta_{ij}$ ? )

 

[PreposterousUniverse]

Not if you don't provide some more context. The way it looks now (to me) it's nonsense ($n_in_j = \delta_{ij}$ ? )

Actually, I think it should be proportional to some symmetrized product of kronecker deltas. But how can one show that?

 

[BvU]

But how can one show that?

First you have to show what you mean. Isn't a unit vector a constant of the integration ?

Describe $\;d\Omega$